Vertical cavity surface emitting laser device

ABSTRACT

A vertical cavity surface emitting laser device includes a first reflective mirror layer, a second reflective mirror layer, and an active layer disposed therebetween, wherein at least one of the first reflective mirror layer and the second reflective mirror layer includes a periodic-refractive-index structure in which the refractive index periodically changes in the in-plane direction and a part of the periodic-refractive-index structure includes a plurality of parts that disorder the periodicity.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a vertical cavity surface emittinglaser (VCSEL).

2. Description of the Related Art

Vertical cavity surface emitting lasers are advantageous in terms oftheir low threshold value, ease of coupling with optical elements,possibility of formation of an array, and the like. Therefore, theVCSELs have been actively studied since the latter half of 1980's.

However, the VCSELs are disadvantageous in that the spot size with whichthe VCSELs can oscillate in the single transverse mode is small, about 3to 4 μm in diameter. The reason for this is as follows. When a VCSELoscillates in the multimode, the responses for an optical element suchas a lens are different from each other in each mode, and the emittedlight does not behave in the same manner.

Furthermore, since the gain region of the VCSEL is small, a pair ofdistributed Bragg reflector (DBR) mirrors constituting a resonator musthave a high reflectance of 99% or more. In order to achieve such a highreflectance, a multilayer film composed of several tens of layers isnecessary in a semiconductor mirror. In such a case, heat is easilyaccumulated in the resonator because of the large layer thickness of themultilayer film. The unsatisfactory heat dissipation effect increasesthe threshold value and the electrical resistance, resulting in adifficulty of current injection and the like.

Fan et al. have reported the wavelength dependence of reflected lightand transmitted light, etc., when a two-dimensional photonic crystalslab is used as a mirror (V. Lousse et al., Opt. Express, Vol. 12, No.15, p. 3436 (2004)).

A photonic crystal has a structure in which a refractive indexmodulation of the order of a predetermined wavelength of light isartificially provided in a material. In other words, in the photoniccrystal structure, media having refractive indices different from eachother are arrayed with a periodicity. It is believed that thepropagation of light in the crystal can be controlled by the multiplescattering effect of the light.

According to the report described in the paper by Fan et al., when lightis incident on a surface of a two-dimensional photonic crystal from adirection substantially perpendicular to the surface, light having apredetermined frequency is reflected with an efficiency of about 100%.

For this reason, the present inventors have studied the use of aphotonic crystal as a mirror layer of a VCSEL.

SUMMARY OF THE INVENTION

By using a photonic crystal mirror as a reflective mirror of a VCSEL, amirror composed of a multilayer film having a large thickness of aboutseveral micrometers can be replaced by a mirror composed of a very thinfilm having a thickness of the order of several tens to several hundredsof nanometers. Consequently, the thermal problem due to the thickness ofthe reflective mirror layer can be suppressed.

However, when the spot size of the emitted light is increased to, forexample, 5 μm or more, the VCSEL cannot oscillate in the singletransverse mode. In other words, an increase in the spot size causes astate that resembles a plurality of lasers having different phasesindependently emitting light. This problem becomes critical when theVCSEL is applied to light condensing with a lens.

The present invention provides a novel VCSEL structure that can easilyoscillate in the single transverse mode.

According to a first aspect, the present invention relates to a verticalcavity surface emitting laser device comprising a first reflectivemirror, a second reflective mirror having a periodic-refractive-indexstructure in which the refractive index periodically changes in thein-plane direction of a plane opposing the first reflective mirror, andan active layer disposed between the first reflective mirror and thesecond reflective mirror. The periodic-refractive-index structureincludes a plurality of parts that disorder the periodicity of theperiodic-refractive-index structure of the second reflective mirror. Theperiodic-refractive-index structure can be a two-dimensional photoniccrystal structure. In addition, a defect level is present within aphotonic bandgap of the two-dimensional photonic crystal structurecorresponding to the parts that disorder the periodicity of theperiodic-refractive-index structure. Further, the parts that disorderthe periodicity of the periodic-refractive-index structure arepositioned periodically or aperiodically in the in-plane direction ofthe second reflective mirror. Also, the parts that disorder theperiodicity of the periodic-refractive-index structure includelight-emitting parts that are optically coupled with each other. In thisembodiment, the vertical cavity surface emitting laser device emitslight in the single transverse mode.

In one embodiment, the first reflective mirror, the active layer, andthe second reflective mirror having the periodic-refractive-indexstructure are disposed on a substrate in that order and the firstreflective mirror comprises a multilayer film. In another embodiment,the second reflective mirror, the active layer, and the first reflectivemirror are disposed on a substrate in that order and the firstreflective mirror comprises a multilayer film. In still anotherembodiment, the first reflective mirror, the active layer, and thesecond reflective mirror having the periodic-refractive-index structureare disposed on a substrate in that order and both the first reflectivemirror and the second reflective mirror comprise a two-dimensionalphotonic crystal. In a further embodiment, the first reflective mirror,the active layer, the second reflective mirror having theperiodic-refractive-index structure, and an electrode are disposed on asubstrate in that order and the periodic-refractive-index structure isnot provided in a part of the second reflective mirror disposed directlyunder the electrode. The second reflective mirror comprises a pluralityof layers each having a periodic-refractive-index structure. In oneembodiment, the periodic-refractive-index structure comprises a firstmedium and a second medium, the second medium having a refractive indexhigher than that of the first medium, and the device further comprises alayer comprising a medium having a refractive index lower than that ofthe second medium disposed between the second reflective mirror havingthe periodic-refractive-index structure and the active layer. The firstreflective mirror can be a distributed Bragg reflector mirror comprisinga multilayer film. In addition, the interval between the parts thatdisorder the periodicity of the periodic-refractive-index structure isset so that the parts that disorder the periodicity serve aslight-emitting parts and light components in each of the parts thatdisorder the periodicity are coupled with each other. In one embodiment,the periodic-refractive-index structure comprises a first area in whichthe parts that disorder the periodicity are disposed and a second areain which the parts that disorder the periodicity are not disposed, andthe second area is positioned so as to surround the first area. In thiscase, the first area comprises a square lattice and the second areacomprises a triangular lattice. Also, the periodic-refractive-indexstructure comprises a two-dimensional photonic crystal and the partsthat disorder the periodicity are defects.

According to a second aspect, the present invention relates to avertical cavity surface emitting laser device comprising a substrate, afirst reflective mirror, an active layer, and a second reflectivemirror. The first reflective mirror, the active layer, and the secondreflective mirror are provided on the substrate. The first reflectivemirror and the second reflective mirror comprise a two-dimensionalperiodic-refractive-index structure. In addition, the laser device emitslight in a single transverse mode.

According to a third aspect, the present invention relates to a verticalcavity surface emitting laser device comprising a substrate, a firstreflective mirror, an active layer, and a second reflective mirror. Thefirst reflective mirror, the active layer, and the second reflectivemirror are provided on the substrate. At least one of the firstreflective mirror and the second reflective mirror comprises atwo-dimensional periodic-refractive-index structure. The spot size ofthe emitted laser light emitted from the vertical cavity surfaceemitting laser device is 5 μm or more. The emitted laser light isemitted in a single transverse mode.

According to a fourth aspect, the present invention relates to avertical cavity surface emitting laser device comprising a substrate, afirst reflective mirror, an active layer, and a second reflectivemirror. The first reflective mirror, the active layer, and the secondreflective mirror are provided on the substrate. At least one of thefirst reflective mirror and the second reflective mirror comprises atwo-dimensional periodic-refractive-index structure. In thetwo-dimensional periodic-refractive-index structure, in a wavelengthrange from 5 to 50 nm, the difference between the reflectance at theresonance wavelength and the reflectance at any other wavelength withinthe wavelength range is within 3%, the wavelength range including theresonance wavelength. In this embodiment, the light emitted from thevertical cavity surface emitting laser device is emitted in a singletransverse mode. In addition, within the wavelength range of 5 to 50 nm,there is a 30 nm wavelength subrange for which the difference betweenthe reflectance at the resonance wavelength and the reflectance at anyother wavelength within that 30 nm wavelength subrange is within 3%, the30 nm wavelength subrange including the resonance wavelength.

According to the present invention, a novel structure of a VCSEL thatcan easily oscillate in the single transverse mode even with anincreased spot size can be provided.

Further features of the present invention will become apparent from thefollowing description of exemplary embodiments with reference to theattached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic cross-sectional view of a laser device including atwo-dimensional photonic crystal according to the present invention.

FIG. 2 is a perspective view of a two-dimensional photonic crystal.

FIG. 3 is a perspective view of a two-dimensional photonic crystal.

FIG. 4 is a schematic diagram showing a photonic band structure.

FIG. 5 is a schematic diagram showing a photonic band of atwo-dimensional photonic crystal in which defects have been introduced.

FIG. 6 is a schematic cross-sectional view showing an embodiment of thestructure of a laser device.

FIGS. 7A and 7B are schematic views of cavity mirrors.

FIG. 8 is a schematic view showing the positional relationship of twocavity mirrors.

FIG. 9 is a schematic cross-sectional view showing an embodiment of thestructure of a laser device.

FIGS. 10A and 10B are schematic views of cavity mirrors in a laserdevice.

FIGS. 11A and 11B are schematic views of cavity mirrors in a laserdevice.

FIG. 12 is a schematic cross-sectional view showing an embodiment of thestructure of a laser device.

FIG. 13 is a schematic cross-sectional view showing an embodiment of thestructure of a laser device.

FIGS. 14A and 14B are schematic views of a periodic structure.

FIG. 15 is a schematic view of a cavity mirror in a laser device.

FIGS. 16A and 16B are schematic views each showing a photonic bandstructure.

FIG. 17 is a schematic cross-sectional view showing an embodiment of thestructure of a two-dimensional photonic crystal surface emitting laser.

FIGS. 18A to 18H are schematic cross-sectional views showing steps ofproducing a two-dimensional photonic crystal mirror.

FIG. 19 is a conceptual cross-sectional view of the two-dimensionalphotonic crystal surface emitting laser.

DESCRIPTION OF THE EMBODIMENTS

A basic structure of a vertical cavity surface emitting laser (VCSEL)according to the present invention will now be described with referenceto FIG. 1.

FIG. 1 is a schematic cross-sectional view of a VCSEL according to thepresent invention. In the figure, the VCSEL includes an active layer1040, spacer layers 1030 and 1050 (also referred to as cladding layers)that sandwich the active layer 1040, electrodes 1020 and 1080, a secondreflective mirror layer 1000, a first reflective mirror layer 1060, anda substrate 1070.

In FIG. 1, a periodic-refractive-index structure is provided in thesecond reflective mirror layer 1000. The periodic-refractive-indexstructure includes parts 1010 that disorder the periodicity. In photoniccrystals, such a part that disorders the periodicity is referred to as adefect in some cases.

The parts that disorder the periodicity of the periodic-refractive-indexstructure can be periodically or aperiodically positioned in thein-plane direction of the first or second reflective mirror layer.

The interval between the parts that disorder the periodicity of theperiodic-refractive-index structure may be determined, for example, sothat the parts that disorder the periodicity serve as light-emittingparts and light components in each of the parts that disorder theperiodicity are coupled with each other.

Furthermore, the first or second reflective mirror layer that has aperiodic-refractive-index structure may include aperiodic-refractive-index structure composed of a plurality of layers.

The periodic-refractive-index structure may include a first medium and asecond medium, the second medium having a refractive index higher thanthat of the first medium. In such a case, a layer that contains a mediumhaving a refractive index lower than that of the second medium may beprovided between the first or second reflective mirror layer that hasthe periodic-refractive-index structure and the active layer.

One of the first and second reflective mirror layers may include theperiodic-refractive-index structure and the other reflective mirrorlayer may be a DBR mirror composed of a multilayer film.

The present invention will now be described in detail.

A periodic-refractive-index structure means a photonic crystal. First,the photonic crystal will be described and defect parts, which are afeature of the present invention, will then be described.

(Photonic Crystal)

A periodic-refractive-index structure (photonic crystal) can beclassified as either a one-dimensional structure, a two-dimensionalstructure, or a three-dimensional structure from the viewpoint of theperiodicity of the refractive index. A multilayer film mirror used forVCSELs has a one-dimensional periodic structure. Since two-dimensionalphotonic crystals (having a periodic structure in which the refractiveindex in the in-plane direction of the structure is periodicallychanged) can be prepared relatively easily, compared withthree-dimensional photonic crystals, the two-dimensional photoniccrystals have been studied most actively heretofore.

Photonic crystals are structures in which a periodic structure ofrefractive index is artificially provided. In particular, structures inwhich a periodicity of refractive index in the periodic structure isprovided in a direction of a plane formed by two axes in spacecoordinates or provided only in two directions that are orthogonal withrespect to each other are referred to as two-dimensional photoniccrystals. There is no periodical change in refractive index in anotherdirection.

In a known form of two-dimensional photonic crystals, aperiodic-refractive-index structure is provided on a thin flat platematerial so as to have a periodicity in the in-plane direction. Suchcrystals are particularly referred to as two-dimensional photoniccrystal slabs.

For example, as shown in FIG. 2, minute holes 1210 are formed on a thinflat plate 1201, which is a semiconductor composed of Si or the like andhaving a high refractive index, with a period approximatelycorresponding to the wavelength of light to be used. Thus, therefractive index can be modulated in the in-plane direction.

As shown in FIG. 3, when light is incident on a two-dimensional photoniccrystal 1300 from a direction substantially perpendicular to the plane(incident light 1301, transmitted light 1302, and reflected light 1303are shown in the figure), the transmission spectra have a complex shape.For example, the above-described document (V. Lousse et al., Opt.Express, Vol. 12, No. 15, p. 3436 (2004)) theoretically describes thefact that the reflectance becomes 100% in three regions at wavelengthsof about 1,100 nm, 1,220 to 1,250 nm, and 1,350 nm. Furthermore, thedocument also describes an experiment in the infrared region thatdemonstrates that the reflectance substantially becomes about 100% as inthe above theory. It is known that the frequency of light to bereflected can be controlled by designing the crystal structure using anumerical simulation by a finite difference time domain (FDTD) method.Despite the presence of such a periodic-refractive-index structure inthe in-plane direction, light incident on the structure from thevertical direction is reflected. This phenomenon is known as in-planeguided resonance. For example, the in-plane guided resonance isdescribed in detail in Physical Review B, Volume 65, 235112. In thepresent invention, a reflective function of a mirror constituting aVCSEL is achieved using this in-plane guided resonance.

Such a phenomenon is based on the fact that light 1301 incident on thetwo-dimensional photonic crystal from a substantially perpendiculardirection is temporarily converted into light guided in the in-planedirection of the photonic crystal, the guided light causes resonance inthe in-plane direction, and the light is emitted again in theperpendicular direction of the side of the incident light. Thisphenomenon will be described with a dispersion relationship (referred toas a “photonic band”) between energy of light guided in thetwo-dimensional photonic crystal and a kinetic momentum.

FIG. 4 is a schematic diagram showing a photonic band of atwo-dimensional photonic crystal. The abscissa indicates a wave numbervector and the ordinate indicates a normalized frequency of light(ωa/2πc: wherein ω represents an angular frequency of light, arepresents a lattice constant of a photonic crystal, and c representslight velocity in vacuum.).

The above-described resonance in the in-plane direction occurs only forlight with a mode of energy higher than the energy of a light cone 41 (aboundary in which guided light in a two-dimensional slab is subjected tototal reflection at the slab interface) in the photonic band structure.In other words, in FIG. 4, the resonance in the in-plane directionoccurs for light present in the upper area relative to the lines of thelight cone 41.

In general, the resonance of light in the in-plane direction is easilyperformed in the multimode. Therefore, when the area of a mirror isincreased (i.e., when the spot size of a laser beam is increased to, forexample, 5 μm or more), the phase of the emitted beam is differentdepending on the position in the in-plane direction.

To overcome this problem, by introducing parts that disorder theperiodicity, which are a feature of the present invention, into aphotonic crystal, single mode light whose phase is aligned can berealized over a large area (for example, 5 to 50 μm in diameter).

In a photonic band diagram as shown in FIG. 4, a frequency band 45 inwhich a photonic band is not present is referred to as a photonicbandgap in imitation of the electron band theory in solid crystals. FIG.5 is a photonic band diagram when parts that disorder the periodicity(hereinafter also referred to as “defect parts”) are disposed in atwo-dimensional photonic crystal. A frequency band (wavelength region)indicated by an area 51 in FIG. 5 indicates a photonic bandgap.

The magnitude of the photonic bandgap is changed depending on thedifference in refractive index between a high refractive index part anda low refractive index part of the photonic crystal. When the differencein the refractive index is large, the photonic bandgap is alsoincreased. When the difference in the refractive index is small, thephotonic bandgap is also decreased. When the difference in therefractive index is excessively small, the photonic bandgap disappears.

In a two-dimensional photonic crystal slab as shown in FIG. 2, themagnitude of the photonic bandgap is changed depending on the dimensionof holes formed in the slab, i.e., a base material, the shape oflattice, the period, and the like.

In two-dimensional photonic crystals, the photonic bandgap in a photoniccrystal having a triangular lattice is generally larger than that of aphotonic crystal having a square lattice. As an approximate standard,when the difference in refractive index is 1.8 or less, the triangularlattice can be used rather than the square lattice because a largephotonic bandgap width can be obtained. Examples of such a substanceinclude GaN and TiO₂.

Both the triangular lattice and the square lattice may be used for asubstance such as Si or GaAs, in which a refractive index difference of1.8 or more can be obtained.

Regarding a structure having a photonic crystal, light of a frequencyband within the photonic bandgap is not present in the structure.However, when defect parts are introduced into the structure, a newlevel (i.e., defect level 52 in FIG. 5) appears within the photonicbandgap and light can be present in the defect parts. In other words,even light within the photonic bandgap can be guided in the crystalthrough the defect parts. The reflection in a two-dimensional photoniccrystal having such defect parts is performed by such light having afrequency of a defect mode.

It is believed that, by introducing defect parts such that no levels arepresent close by, light components present in the defect level (i.e.,localized light components in the defect parts) interact strongly andare coupled with each other. As a result, oscillation is easilyperformed in the single transverse mode. Thus, a plurality of parts thatdisorder the periodicity is introduced into a periodic-refractive-indexstructure. Consequently, a VCSEL that emits light whose phase is alignedcan be provided even when the spot size is large, for example, the spotsize is in the range of 5 to 50 μm.

Embodiments below describe VCSELs that have a spot size of 15 μm andoscillate in the single mode.

The present invention provides a structure that easily oscillates in thesingle mode. The field of application of the present invention is notlimited to a VCSEL having a spot size of 5 to 50 μm. In addition,although the description of a two-dimensional photonic crystal hasmainly been made, the present invention can also be applied to athree-dimensional photonic crystal.

The position and the size of the parts that disorder the periodicity ofa periodic-refractive-index structure (defect parts) in the presentinvention are not particularly limited. However, as described above, anew level must be formed within the photonic bandgap by introducing thedefect parts.

The interval between a plurality of defect parts introduced in theperiodic-refractive-index structure must be determined so that lightcomponents can be present on the introduced defect parts and the lightcomponents present on each of the defect parts can be coupled with eachother. In other words, a plurality of defect parts is arrayed with suchan interval that the distributions of light intensity mainly obtainedfrom the introduced defect parts have an area where the distributionsoverlap with respect to each other.

The interval depends on the material and the structure of the photoniccrystal, and the wavelength region of light to be guided. For example,in the case of a photonic crystal prepared by forming holes on a slab soas to form a triangular lattice (period a), a photonic crystal having arefractive index of about 3.5, a slab thickness of 0.5a, and a holediameter of 0.4a, an interval between the defect parts can be, forexample, from two to eight periods. The term “period” means the periodof a periodic-refractive-index structure. Here, normalization isperformed with a lattice constant, and a condition relating to only theperiod is described as an example.

Furthermore, the period of the periodic-refractive-index structure andthe interval between a plurality of defect parts to be introduced alsodepend on the design of the oscillation wavelength. For example, in thecase of laser beam having a wavelength of 670 nm, the period of theperiodic-refractive-index structure is set to 180 nm in the in-planedirection and a part that does not include a hole (defect part) isdisposed every three periods. In this case, oscillation in the singletransverse mode can be performed even with a spot size of 15 μm. Theperiodic-refractive-index structure may have a period corresponding tothe wavelength of light emitted from an active layer or an integralmultiple of the emission wavelength.

The interval between the defect parts can be appropriately determined,for example, in the range from 2 times or more (i.e., two periods ormore) to 50 times or less, 20 times or less, or further 10 times or lessof the period of the periodic-refractive-index structure. When a film islaminated on the periodic-refractive-index structure, a structure thatdoes not use the dielectric constant of air or vacuum, that is, astructure that does not use the air-gap can also be used.

(Method for Introducing Defect Parts)

Referring to an example of the two-dimensional photonic crystal in FIG.2, as described above, the holes 1210 are partially removed (that is,further holes are not formed or some of existing holes are filled), orholes having a dimension different from that of other surrounding holesare formed, thereby forming the defects.

Alternatively, another substance having a different refractive index (asolid material other than air) may be introduced into the parts used asthe defects, thereby forming the defects.

The degree of disorder of the periodicity of the photonic crystal iscontrolled by introducing the defect parts. Thereby, the defect level ina photonic band diagram can be disposed at the center of the photonicbandgap. For example, in the example of the two-dimensional photoniccrystal in FIG. 2, the control is achieved by tuning the diameter of theholes in the defect parts to an appropriate value. However, when thedegree of disorder of the periodicity due to the introduction of thedefect parts is excessively small, the defect level is disposed at aposition close to a band edge of the photonic bandgap.

When the defect mode is close to the band edge, the difference in energybetween the defect mode and a mode of the band edge or the inside of theband becomes small, and thus a plurality of modes including the defectmode may be disposed in the gain region of a laser active layertogether. In such a case, the selectivity of modes is degraded, whicheasily results in phenomena that oscillation is performed in a pluralityof modes at the same time and a plurality of modes is unstably switched.

Therefore, from the standpoint of easily controlling the oscillationmode, the defect level can be present at the center of the photonicbandgap. Specifically, the defect level is designed so as to be disposedwithin the photonic bandgap.

The defect level is designed so as to be present within the central 70%,50%, or 30% of the photonic bandgap, i.e., a region within an areaextending on either side of the center of the photonic bandgap so as toencompass 70%, 50%, or 30% of the area of the photonic bandgap and so asto be spaced from the band edge of the photonic bandgap.

(Types of Defect Parts)

Regarding a plurality of defect parts of a photonic crystal introducedin at least one mirror constituting a resonator of a VCSEL, the defectpart itself may have a periodicity (periodic defect) or may not have anyperiodicity (aperiodic defect).

Herein, the term “periodic defect” means the case where the positionsfor introducing the defects spatially have transitional symmetry. Such aperiodic defect can be often introduced by merely changing therefractive index value without changing the spatial arrangement of theperiodic-refractive-index structure in which the defects have yet notintroduced. For example, in the two-dimensional photonic crystal in FIG.2, a photonic crystal in which a defect (a place where a hole is notprovided) is provided for every two periods of holes is an example ofthe periodic defect.

In this case, the period of the defects can be freely changed. Asdescribed above, the defect period can be appropriately adjusted so thatlight components localized in the defect parts are coupled with eachother. The period of the defects may have anisotropy relative to adirection of a primitive lattice.

The term “aperiodic defect” means the case where the distribution of thedefects does not have spatial transitional symmetry but the defects aredisposed so as to have a certain type of regularity. For example, thedefects may be distributed on the basis of a certain type ofmathematical pattern, or the structure may have a quasi-crystallinestructure that does not have symmetry locally but has symmetry over along period. An embodiment of the case where the distribution of thedefects has a mathematical pattern will be described in a thirdembodiment. In addition to a point defect having a size corresponding toone lattice point, a line defect in which defect parts are continuouslyconnected, or a defect in which three or more point defects continuouslyform one defect (referred to as large point defect) may also be used. Insuch a case, at the line defect or the large point defect part, thepoint defects are connected to each other. Therefore, the intervalbetween the defects corresponds to one period. However, the line defectsor the large point defects are arrayed with an interval of about 2 to 8periods, and thus the localized light components are coupled with eachother. In addition, these three types of defect, i.e., the point defect,the line defect, and the large point defect may be combined. Introducingdefects also provides the following effect. By introducing defects, thedistribution of refractive index on the mirror can be controlled tochange the mode pattern of the emitted light. In other words, the modepattern of the emitted light is changed by changing the type of thedefects. Thus, the far-field pattern of the laser beam can be varied.Such an effect can be achieved even when the interval between thedefects is not set to a distance in which the localized light componentsare coupled with each other.

The periodic-refractive-index structure in the present invention may beas follows. That is, the periodic-refractive-index structure in thesecond reflective mirror includes a first layer and a second layer.Specifically, the first layer has a structure in which the refractiveindex periodically changes in the in-plane direction, and the secondlayer includes a part that disorders the periodicity of theperiodic-refractive-index structure.

The first layer and the second layer are disposed in the vicinity of anactive layer constituting a surface emitting laser. The part thatdisorders the periodicity of the refractive index of the two-dimensionalphotonic crystal is formed in the second layer. In the presentinvention, it is sufficient that the second layer itself functions as adefect. The structure (e.g., holes) in the second layer does notnecessarily have a periodicity. The phrase “in the vicinity” of theactive layer means a range in which light generated in the active layerhas an optical effect.

To produce such a surface emitting laser device, in the presentinvention, the first layer and the second layer may form the followingstructure. Specifically, the first layer may have a firsttwo-dimensional periodic structure layer in which columnar structurescomposed of a second medium having a second refractive index areperiodically provided at a certain interval in a first medium having afirst refractive index. The second layer may have a two-dimensionalperiodic structure layer in which columnar structures composed of afourth medium having a fourth refractive index are provided in a thirdmedium having a third refractive index. These layers are formed so thatthe interval of the columnar structures in the second layer is differentfrom the periodicity of the columnar structures in the above firsttwo-dimensional periodic structure layer. Furthermore, the shape,dimensions, and the like of the columnar structures in the second layeris different from those of the columnar structures in the firsttwo-dimensional periodic structure layer. The arrangement of thecolumnar structures in the second layer does not necessarily require aperiodicity.

In this case, the second medium having the second refractive index andthe fourth medium having the fourth refractive index may be the samemedium. Furthermore, the first medium having the first refractive indexand the third medium having the third refractive index may be the samemedium, and the second medium having the second refractive index and thefourth medium having the fourth refractive index may be the same medium.The first medium having the first refractive index and the third mediumhaving the third refractive index may be a semiconductor layer, and thesecond medium having the second refractive index and the fourth mediumhaving the fourth refractive index may be air Either the second mediumhaving the second refractive index or the fourth medium having thefourth refractive index may be a porous semiconductor layer.

(Materials of Structure Having a Photonic Crystal)

Any of metals, semiconductors, and dielectric materials may be used fora two-dimensional photonic crystal mirror, but materials, such assemiconductors and dielectric materials that transmit light having awavelength of laser oscillation can be mainly used. When oscillation isperformed by optical-pumping, both semiconductors and dielectricmaterials may be used. When oscillation is performed by currentinjection, semiconductors can be used.

Two-dimensional photonic crystals have a structure in which a lowrefractive index part and a high refractive index part are periodicallyarrayed. A structure including a high refractive index part composed ofa semiconductor having a high refractive index, such as silicon, and alow refractive index part composed of a hole can provide the largestdifference in refractive index. In other words, such a structure canachieve a large photonic bandgap.

When current injection is performed through such a two-dimensionalphotonic crystal mirror, the low refractive index part can be composedof a semiconductor having a refractive index lower than that of thematerial used in the high refractive index part.

The thickness in the direction perpendicular to theperiodic-refractive-index structure of a two-dimensional photoniccrystal (the direction in which the periodic-refractive-index structureis not present) will be described. The thickness is determined so thatthe transverse mode of light guided in a crystal in the two-dimensionalin-plane direction is single. Although the thickness varies depending onthe wavelength of light to be guided and the material constituting thephotonic crystal, it can be derived by a known calculation method (see,for example, “Hikari doharo no kiso” (Fundamentals of opticalwaveguides) (by Katsunari Okamoto, The Optronics Co., Ltd.), Chapter 2).For example, the case where a silicon photonic crystal is used and asubstance outside the photonic crystal is air will be described. Thethickness of the photonic crystal is controlled to 220 nm or less forguided light with a wavelength of 1.5 μm, thereby achieving the singletransverse mode.

The medium outside the photonic crystal in the direction perpendicularto the periodic-refractive-index structure of the two-dimensionalphotonic crystal (the thickness direction, i.e., the emitting directionof the VCSEL) may be composed of air or any other material. However,when the oscillation is performed by current injection, the medium canbe composed of a material having a refractive index lower than that of amaterial having a higher refractive index among materials constitutingthe photonic crystal so that light is effectively confined in thetwo-dimensional photonic crystal and a carrier is injected from anelectrode on a mirror to an active layer. Furthermore, the refractiveindex of the medium outside the two-dimensional photonic crystal can bethe same as that of the photonic crystal. However, as described above,the structure including air, i.e., another medium, may be asymmetric. Inthis case, the refractive index of the outside medium can be lower thanthat of the material with high refractive index constituting thephotonic crystal.

In addition, the light-emitting parts in the parts that disorder theperiodicity of the periodic-refractive-index structure can be disposedwith an interval in which the light-emitting parts are optically coupledwith each other, and the vertical cavity surface emitting laser deviceemits light in a single transverse mode.

In a specific VCSEL structure, the first reflective mirror, the activelayer, and the second reflective mirror having theperiodic-refractive-index structure are disposed on a substrate in thatorder and the first reflective mirror is composed of a multilayer filmmirror (DBR mirror).

In another VCSEL structure, the second reflective mirror having theperiodic-refractive-index structure, the active layer, and the firstreflective mirror are disposed on a substrate in that order and thefirst reflective mirror is composed of a multilayer film mirror.Alternatively, both the first reflective mirror and the secondreflective mirror may be composed of a two-dimensional photonic crystal.

When the first reflective mirror, the active layer, the secondreflective mirror having the periodic-refractive-index structure, and anelectrode are provided on a substrate in that order, the device can havethe following structure from the viewpoint of the current injection.

Namely, the periodic-refractive-index structure is not provided in apart of the second reflective mirror disposed directly under theelectrode.

The periodic-refractive-index structure may include a first area inwhich the parts that disorder the periodicity are disposed and a secondarea in which the parts that disorder the periodicity are not disposed,and the second area may be positioned so as to surround the first area.

In particular, the first area can be composed of a square lattice andthe second area can be composed of a triangular lattice.

In the present invention, defects are not necessarily introduced in theperiodic-refractive-index structure as long as light emits in the singletransverse mode. Accordingly, the present invention includes thefollowing structure. Namely, a vertical cavity surface emitting laserdevice includes a substrate; a first reflective mirror; an active layer;and a second reflective mirror, the first reflective mirror, the activelayer, and the second reflective mirror being provided on the substrate,wherein the first reflective mirror and the second reflective mirrorinclude a two-dimensional periodic-refractive-index structure, and thedevice emits laser light in a single transverse mode.

The present invention also includes the following structure. Namely, avertical cavity surface emitting laser device includes a substrate; afirst reflective mirror; an active layer; and a second reflectivemirror, the first reflective mirror, the active layer, and the secondreflective mirror being provided on the substrate, wherein at least oneof the first reflective mirror and the second reflective mirror includesa two-dimensional periodic-refractive-index structure, the spot size ofthe emitted light is 5 μm or more, and the emitted light is the singletransverse mode.

The present invention also includes the following structure. A verticalcavity surface emitting laser device includes a substrate; a firstreflective mirror; an active layer; and a second reflective mirror, thefirst reflective mirror, the active layer, and the second reflectivemirror being provided on the substrate, wherein at least one of thefirst reflective mirror and the second reflective mirror includes atwo-dimensional periodic-refractive-index structure. In thetwo-dimensional periodic-refractive-index structure, in a wavelengthrange of from 5 to 50 nm, the difference between the reflectance at theresonance wavelength and the reflectance at any wavelength within thewavelength range is within 3%, the wavelength range including theresonance wavelength, and the light emitted from the vertical cavitysurface emitting laser device is emitted in a single transverse mode.

A photonic crystal having a periodic structure in the in-plane directionis irradiated with light from a direction perpendicular to the in-planedirection. When the reflectance or the transmittance is measured whilethe wavelength (or the frequency) is varied, a wavelength at which thereflectance is about 100% is present. This wavelength is generallyreferred to as “resonance wavelength”. When light having the resonancewavelength is incident on the photonic crystal, the light is temporarilyguided in the in-plane direction and then returns as reflected light.

The reflectance at the resonance wavelength is approximately 100%.However, in general, when the wavelength is shifted from the resonancewavelength by about 1 nm, the reflectance is drastically decreased by20% or more. When the above reflex action at the resonance wavelength isapplied to a mirror of a VCSEL, considering the margin for errors inproduction, a wavelength range for which the ratio of change in thereflectance relative to the reflectance at the resonance wavelength iswithin 3% must be in the range from about 5 to 50 nm.

A photonic crystal in which the change in the reflectance is suppressedwithin about 3% in a wavelength range of 30 nm, the range including theresonance wavelength, is described in a paper by Fan et al. (OpticsExpress, Vol. 12, No. 8 (2004), pp. 1575-1582). From the viewpoint ofthe production of VCSELs, such a photonic crystal mirror can be used.

Some characteristic structures of the present invention will now bedescribed.

(The Case where Cavity Mirrors Constituting a VCSEL are Composed of aMultilayer Film Mirror and a Photonic Crystal)

The following case will now be described. Among a pair of mirrors in aresonator of a laser device, one of the mirrors is a multilayer filmmirror and the other mirror is composed of a photonic crystal includingthe above-described defect parts.

Regarding a pair of reflective mirrors constituting a resonator of thesurface emitting laser device of the present invention, when one of themirrors has a periodic-refractive-index structure in which defects havebeen introduced, any mirror may be used as the other mirror. Of course,both layers formed on and under an active layer may be composed of aphotonic crystal.

A structure in which a distributed Bragg reflector (DBR) mirror used ina known VCSEL is used as one of the mirrors will be described. A mirrorhaving the structure that has been described above can be used withoutfurther treatment as the mirror having the periodic-refractive-indexstructure in which defects have been introduced. All the above-describedstructures relating to the pattern of the periodic-refractive-indexstructure, the variation of the defects, and the like may be used.

A DBR mirror used in a normal VCSEL or the like can be used as amultilayer film mirror in the present invention. The DBR mirror isgenerally prepared by alternately laminating two types of materialhaving different refractive indices. The thickness d of one layer ineach medium is designed so that an equation represented by Nd=λ/4 (N:refractive index of medium, λ: wavelength of resonating light) issatisfied. Examples of the materials used in the DBR mirror includemetals, dielectric materials, and semiconductors. Considering opticalabsorption by metals, dielectric materials and semiconductors can beused. In addition, when driving is performed by current injection,metals having low electrical resistance and semiconductor materials canbe used.

Specific examples thereof include materials that have relatively closelattice constants with respect to each other, such asIn_(x)Ga_(1-x)As_(y)P_(1-y)/In_(x′)Ga_(1-x′)As_(y)P_(1-y′),Al_(x)Ga_(1-x)As/Al_(y)Ga_(1-y)As, and GaN/Al_(x)Ga_(1-x)N. In order toincrease the reflectance of this mirror, it is necessary that thedifference in refractive index between the two types of material is aslarge as possible and the number of laminated layers is large. However,in the case where the mirror is produced using a conductive material,when the number of laminated layers is increased, the electricalresistance in the direction perpendicular to the surface of thelaminated film increases. In order to successfully inject current intothe device through the mirror, the electrical resistance of the mirroris required to be low. Therefore, in this case, a desired reflectance isrequired to be obtained under the condition that a large difference inrefractive index between the two types of material of the mirror isensured while the number of laminated layers is kept as small aspossible. Furthermore, when a mirror is used as a reflective mirror of asurface emitting laser cavity, the mirror may be produced by onlycrystal growth without other processes such as cladding. Accordingly,the material of the mirror may have a lattice constant close to that ofthe material constituting the main part of the laser device.

Both mirrors disposed on and under an active layer may be composed of aphotonic crystal. In such a case, one of the mirrors may be composed ofa photonic crystal in which no defects have been introduced and theother mirror may be composed of a photonic crystal having defects. Whena photonic crystal is used as a mirror, the photonic crystal can be usedfor an upper mirror disposed opposite to a lower mirror with the activelayer therebetween rather than the lower mirror disposed between asubstrate and the active layer. The reason for this is that when aperiodic-refractive-index structure is formed using holes, a smallernumber of films formed on the structure can simplify the productionprocess. Needless to say, one of the mirror layers disposed on and underthe active layer may be composed of a photonic crystal and the othermirror layer may be composed of a multilayer film (DBR) including layerswhose refractive indices are different from each other.

(The Case where the Mirror is Composed of a Multilayer Film Having aPlurality of Periodic-Refractive-Index Structures)

In the surface emitting laser device of the present invention, theperiodic-refractive-index structure constituting a pair of reflectivemirrors of a resonator may be composed of a single structure (with oneperiod) or may have a structure in which a plurality of types of such asingle structure are combined.

For example, the case where the periodic-refractive-index structure iscomposed of a two-dimensional photonic crystal will be considered. Atwo-dimensional photonic crystal mirror constituting the resonator maybe composed of a plurality of layers laminated in the resonatingdirection of light in the resonator (emitting direction, hereinafterdescribed as resonance in the vertical direction) to form at least oneof the cavity mirrors. Instead of the two-dimensional photonic crystal,a three-dimensional photonic crystal may also be used. A spacer layercomposed of air or another medium may be provided between aperiodic-refractive-index structure region having a certain periodicityand another periodic-refractive-index structure region having anotherperiodicity. Thus, the cavity mirror may have a structure of amultilayer film mirror in which a pair of layers including theperiodic-refractive-index structure layer and the spacer layer forms oneperiod.

The pair of the layers is required to be designed so that the phases oflight resonating in the mirror are matched. Specifically, there are twoconditions for the phase matching: First, the positional relationship ofthe periodic-refractive-index structures in the direction parallel tothe resonating direction of light resonating in the two-dimensionalphotonic crystal (i.e., the direction perpendicular to the emittingdirection of light, this direction is referred to as the horizontaldirection) is constant. Secondly, the thickness of the pair of layers isadjusted while the first condition is satisfied.

The first condition should be considered when the thickness of thespacer layer provided between periodic-refractive-index structure layersis small and two or more of the periodic-refractive-index structures areoptically coupled with each other. In such a case, an alignment(parallel shift or rotation) of the periodic-refractive-index structuresin the horizontal direction is required. If these positions are notaligned, the phases of light emitted from the periodic-refractive-indexstructures in the vertical direction are different from each layer,resulting in a decrease in the reflectance. Even when the thickness ofthe spacer layer is large and the periodic-refractive-index structuresare not optically coupled with each other, the positional relationshipcan be constant.

Regarding such a positional relationship, for example, when a pluralityof two-dimensional photonic crystal slabs having the same period arelaminated, the positions of holes are matched with an accuracy within anerror of 3 nm.

The second condition can be satisfied by adjusting the thickness of thepair of layers while the first condition is satisfied. As describedabove, when the thickness of the periodic-refractive-index structurelayer is excessively large, the mode in the vertical direction in thelayer disadvantageously becomes a multimode. Accordingly, the thicknessof the periodic-refractive-index structure layer may be fixed and onlythe thickness of the spacer layer may be changed to adjust the totalthickness. In order to obtain a large difference in refractive indexbetween the spacer layer and the periodic-refractive-index structure andto increase the reflectance, the spacer layer can be composed of air.When current injection is performed through the mirror, the material ofthe spacer layer can be a metal or a semiconductor. However, consideringoptical absorption by metals, the spacer layer can be composed of asemiconductor in order to decrease the threshold of the laser.

Use of the above cavity mirror composed of a plurality ofperiodic-refractive-index structures can increase the reflectancecompared with a mirror composed of a single periodic-refractive-indexstructure.

(Active Layer and Spacer Layer (Cladding Layer))

As an active layer and a spacer layer that constitute a resonator, adouble hetero-structure, a multiple quantum well structure, a quantumdot structure, or the like, which is used in normal VCSELs, can bedirectly applied. When the refractive index of the mirror is higher thanthat of the cladding layer, the length L of the resonator (the distancebetween cavity mirrors) represented by the thickness of the activelayer+the thickness of cladding layers must be designed so that therelationship of NL+ΔL=nλ/2 (N: refractive index of resonator medium, n:positive integer, λ: wavelength of resonating light, ΔL: change in theoptical path length by the phase shift during mirror reflection) issatisfied. Furthermore, the active layer can be disposed at the antinodeof standing waves formed in the resonator.

Examples of the materials of the active layer and the cladding layerinclude materials of those used in known VCSELs, such as GaAs/AlGaAs,InGaAsP/InP, AlGaInP/GalnP, GaN/InGaN/AlGaN, and GaInNAs/AlGaAs. In anexample of the structure, n- and p-type GaN layers are used for thecladding layers disposed on either side of the active layer and anon-doped GaN/InGaN multiple quantum well structure is used for theactive layer.

(Method of Carrier Injection to Active Layer)

Regarding a method of carrier injection to the active layer 1040, forexample, carrier injection to the active layer is performed by currentinjection from an electrode including a pair of an anode and a cathode.

Examples of the electrode that can be used include a ring electrode,which is used in normal VCSELs, and electrodes having various shapessuch as a circle and a rectangle.

When the periodic-refractive-index structure is composed of a solidmedium with holes, a pattern of the periodic structure is not formed onan area disposed directly under the electrode. The reason for this isthat the contact resistance may increase because of the presence of theholes.

The material of the electrode depends on the laser device material ofthe area on which the electrode is formed.

For example, Au—Ge—Ni or Au—Sn may be used for the electrode on ann-type GaAs layer and Au—Zn or In—Zn may be used for the electrode on ap-type GaAs layer. A transparent electrode, such as indium tin oxide(ITO), may also be used. In particular, when an electrode other than aring electrode is formed on a light-emitting surface of the device, atransparent electrode can be used.

(A Structure in which a Medium Having a Refractive Index Lower than thatof a Medium Having the Highest Refractive Index Among the MediaConstituting a Periodic-Refractive-Index Structure is Introduced atPositions Adjacent to the Periodic-Refractive-Index Structure of aReflective Mirror with an Interval Smaller than the Period of thePeriodic-Refractive-Index Structure)

In the surface emitting laser device of the present invention, a lowrefractive index medium may be introduced at positions adjacent to aperiodic-refractive-index structure of a reflective mirror with aninterval smaller than the period of the periodic-refractive-indexstructure. Thereby, the effective refractive index at the positions canbe decreased. The low refractive index medium to be introduced must havea refractive index lower than that of a medium having the highestrefractive index among the media constituting theperiodic-refractive-index structure of the reflective mirror. Forexample, in a two-dimensional photonic crystal prepared by periodicallyforming holes on silicon (Si), a medium having a refractive index lowerthan that of Si serving as a base material may be introduced with aninterval smaller than the period of the holes. A structure in which thismedium is composed of air can be achieved by allowing a materialadjacent to the photonic crystal to be porous. This structure canprevent light guided in the periodic-refractive-index structure fromleaking to the outside. Consequently, the light can be effectivelyconfined in the periodic-refractive-index structure.

Any medium may be introduced as long as the medium has a refractiveindex lower than that of a medium having the highest refractive indexamong the media constituting the periodic-refractive-index structure.The structure in which the medium is composed of air, in other words,the structure prepared by forming a porous structure containing holescan be used because such a structure can provide a large difference inrefractive index with the medium that has the highest refractive indexand that constitutes the periodic-refractive-index structure, andimprove the efficiency of light confinement in theperiodic-refractive-index structure.

The VCSEL according to the present invention can be used as variouslight sources for light emission. An array of the VCSELs may also beused as a multi-beam light source. For example, the present inventioncan be applied to an image forming apparatus disclosed in JapanesePatent Laid-Open No. 2004-230654. Examples of the image formingapparatus include a copy machine, a laser beam printer, and a facsimilemachine wherein a laser beam from a laser light source, the laser beambeing subjected to light modulation, is guided on an image-carryingsurface such as a photoreceptor or an electrostatic recording medium andimage information composed of, for example, an electrostatic latentimage is formed on the surface. Hitherto, when a VCSEL is used as alight source, the maximum output is low and thus the luminous power isinsufficient in a structure in which a laser beam passes through aplurality of optical systems such as a polygon scanning mirror.According to the present invention, since the size of emission spot canbe increased to 5 μm or more, the VCSEL of the present invention can beused as a surface emitting laser with high output.

Embodiments of the present invention will now be described.

Embodiments described below are illustrative and conditions such as thestructural materials, the dimensions, and the shapes of laser devicesused in the present invention are not limited to the following first tosixth embodiments.

First Embodiment

The structure of a laser device according to a first embodiment will nowbe described with reference to FIG. 6.

A lower cavity mirror light confinement layer 62, a lower cavity mirrorlayer 63, a lower cladding layer 64, an active layer 65, an uppercladding layer 66, and an upper cavity mirror layer 67 are sequentiallylaminated on a substrate 61. An n-electrode 68 and a p-electrode 69 areprovided on the reverse face of the substrate 61 and on the top face ofthe upper cavity mirror layer 67, respectively.

The substrate 61 is an n-type GaAs substrate having a thickness of 565μm. The lower cavity mirror light confinement layer 62 is composed ofn-type Al_(0.7)Ga_(0.4)As and has a thickness of 1 μm. The lower cavitymirror layer 63 is composed of n-type Al_(0.4)Ga_(0.6)As and the lowercladding layer 64 is composed of n-type(Al_(0.5)Ga_(0.5))_(0.5)In_(0.5)P. The upper cavity mirror layer 67 iscomposed of p-type Al_(0.4)Ga_(0.6)As and the upper cladding layer 66 iscomposed of p-type (Al_(0.5)Ga_(0.5))_(0.5)In_(0.5)P.

Photonic crystal structures 610 and 612 forming mirrors are provided atthe centers of the lower and upper cavity mirror layers 63 and 67,respectively. Defects 611 are introduced only in the lower mirror.

The distance between the lower and upper cavity mirror layers 63 and 67(i.e., the length of the resonator) is about 1.5 μm (corresponding toabout 7.5 times the wavelength of resonating light of 670 nm). Theactive layer 65 has a strained quantum well structure composed ofnon-doped In_(0.56)Ga_(0.44)P/(Al_(0.5)Ga_(0.5))_(0.5)In_(0.5)P. Thenumber of layers of the well is three. Each of the In_(0.56)Ga_(0.44)Player and the (Al_(0.5)Ga_(0.5))_(0.5)In_(0.5)P layer has a thickness of6 nm. The n-electrode 68 adjacent to the substrate is composed ofNi/Au/Ge and the p-electrode 69 adjacent to the mirror is composed ofAu—Zn.

The above laminated film can be produced by the following steps. AnAl_(0.9)Ga_(0.4)As lift-off layer is formed on a GaAs substrate by ametalorganic chemical vapor deposition (MOCVD) method. Layers includingthose from the upper cavity mirror layer to the lower cavity photoniccrystal mirror layer are sequentially formed on the lift-off layer byMOCVD. Since the GaAs substrate, which has been used for the firstgrowth, must be lifted off in a later process, the lift-off layer isinterposed between the substrate and the upper cavity mirror. The layersincluding those from the upper cavity mirror layer to the lower cavitymirror layer are then sequentially formed on the lift-off layer. First,the lower cavity mirror is formed. A photonic crystal pattern of thelower cavity mirror is formed by electron beam (EB) lithography andreactive ion beam etching (RIBE) using Cl₂ gas. A wafer is prepared byforming the lower cavity mirror light confinement layer with a thicknessof 1 μm on a separate GaAs substrate. The surface of the lower cavitymirror layer and the surface of the lower cavity mirror lightconfinement layer are aligned and joined by thermal fusion bonding.Thus, the formation of the lower cavity mirror is completed. Next, theupper cavity mirror is formed. The Al_(0.6)Ga_(0.4)As lift-off layeradjacent to the upper cavity mirror layer is selectively etched withhydrofluoric acid to remove the GaAs substrate, which has been used forthe first growth. A photonic crystal pattern is formed on the exposedupper cavity mirror layer by the same method as that used to form thepattern on the lower cavity mirror layer. Thus, the formation of theupper cavity mirror is completed. Finally, the n-electrode and thep-electrode are formed on the reverse face of the GaAs substrate and onthe upper cavity mirror layer, respectively, by vapor deposition.

The photonic crystal mirrors of the lower and upper cavity mirrors willnow be described in detail.

FIGS. 7A and 7B are plan views of the photonic crystals of the lower andupper mirrors, respectively. The photonic crystal structure is formed byperiodically providing holes 71 or 74 in the Al_(0.4)Ga_(0.6)As layer.For example, as described above, such fine holes can be formed on theAl_(0.4)Ga_(0.6)As layer by transferring a pattern formed by EBlithography by dry etching.

In both the lower and upper mirror layers, the holes each have a roundshape and are arrayed in a triangular lattice with a period of 180 nm.The radius of the holes is 75 nm and the thickness of the layer is 270nm. Hereinafter, a photonic crystal structure in which no defect hasbeen introduced is defined as a basic (or host) photonic crystalstructure.

No defects are introduced to the upper photonic crystal mirror in FIG.7B. In contrast, as shown in FIG. 7A, defects 72 that disorder theperiodic-refractive-index structure of the photonic crystal areperiodically introduced to the lower photonic crystal mirror.

The defects 72 are formed by periodically removing the hole of the basicphotonic crystal. The defects 72 form a triangular lattice as in thebasic photonic crystal structure, but the interval between the defectscorresponds to three periods of the basic photonic crystal structure.Although the number of periods of the holes of the photonic crystal inFIGS. 7A and 7B is smaller than that in the actual mirror area for thesake of convenience, the basic photonic crystal and the defect areintroduced over 80 periods or more in the actual mirror area.

In this embodiment, the defects of the lower photonic crystal mirror areformed by periodically removing the hole in the basic photonic crystalstructure. Alternatively, a hole having a size different from that ofthe hole in the basic photonic crystal may be used. Alternatively, thedefects may be formed by introducing another material having a differentrefractive index into the defect parts.

Regarding the array of the defects, the interval between the defects inthis embodiment corresponds to three periods of the photonic crystalstructure. The interval may be larger or smaller than this. However,when the interval is excessively large, light components localized inthe defects cannot be coupled with each other. Therefore, an upper limitof the interval is present.

In this embodiment, the defects are provided only on the lower mirroramong the two upper and lower photonic crystal mirrors. Alternatively,the defects may be introduced to only the upper mirror or both the upperand lower mirrors.

Furthermore, the positional relationship between two upper and lowermirrors will be described. FIG. 8 is a view showing the relativepositional relationship of an upper cavity mirror 81 and a lower cavitymirror 82 that constitute a resonator.

The figure represents a possible relative positional relationshipobtained by moving the lower cavity mirror 82 in the directions ofcoordinates shown by the arrows, for the sake of convenience. As shownin FIG. 8, the relative positional relationship between the two mirrorsis determined in terms of a total of six directions including orthogonaldirections of the x, y, and z directions and the α, β, and γ directions,which are directions rotating around the x, y, and z axes, respectively.Each of the directions will now be described in order.

Regarding the x direction and the y direction, conditions required forthe positional relationship are significantly different depending on thedistance between the two mirrors. Specifically, the conditions depend onthe distance between the two mirrors in the z direction. When the twomirrors are separated from each other to only such an extent that lightcomponents guided in the in-plane directions of the mirrors can becoupled with each other, the characteristics of the resonator markedlychange according to the positional relationship in the x and ydirections of the mirrors. Consequently, since the positionalrelationship in the x and y directions of the mirrors significantlyaffects the resonance characteristics, the positional relationship inthe x and y directions must be kept constant in order to ensure that thecharacteristics of the laser device are produced constant. Even when thedistance between the mirrors is larger than that in the above case, thepositional relationship can be maintained constant. The distance isdetermined by the materials of the resonator, the materials of themirror, and the wavelength of the resonating light. The resonator ofthis embodiment has a large distance in the z direction so as to preventguided light components in the mirrors from coupling with each other.Regarding the γ direction, since the mirrors in the present embodimentdo not have a polarization dependence with respect to each other, thepolarization property of the emitted light is not particularly affectedby the rotation in the γ direction. However, the positional relationshipcan be maintained constant in this case. The distance in the z directionis adjusted so that the distance L between the two reflective mirrorssatisfies the above-described resonating conditions as in a normal VCSELresonator. The rotations in the α and β directions are required to bereduced as much as possible and are ideally zero so that the two mirrorsare completely parallel with respect to each other. However, when theentire laser device in this embodiment can be produced at one time bycrystal growth, the rotations in these directions hardly occur, and thusno special adjustment is required.

The lower cavity mirror light confinement layer 62 and the claddinglayers 64 and 66 in this embodiment are formed so that the resonatinglight converted into the guided light of the in-plane direction iseffectively confined inside the mirror. Specifically, Al_(0.7)Ga_(0.4)Ashaving a refractive index lower than that of Al_(0.4)Ga_(0.6)As, whichis the material of the mirrors, is used. For this purpose, for example,the cladding layers may be composed of Al_(0.4)Ga_(0.6)As, which is thesame material as that of the cavity mirror layers, and the claddinglayers may have a structure in which a large number of holes that aresufficiently smaller than the holes constituting the photonic crystal ofthe mirrors are provided (i.e., porous structure). This structure candecrease the effective refractive index at this area, and thus theresonating light converted into the guided light of the in-planedirection can be easily confined inside the mirror. Furthermore, sincethis structure can decrease the length of permeation of the light guidedin the in-plane direction of the mirrors into the cladding layers, aneffect of coupling with the active layer can also be decreased.Consequently, the length of the resonator can be reduced. Referring toFIGS. 7A and 7B, in both lower and upper cavity mirrors, currentinjection areas 73 and 75 are respectively provided around the lightreflection area composed of the above-described two-dimensional photoniccrystal slab. In order to reduce the electrical resistance, holes arenot provided in the current injection areas 73 and 75. Therefore, onlythe area including the photonic crystal structure functions as themirror. The mirror area has a round shape with a diameter of 15 μm.

In this embodiment, a current narrowing structure is formed byincreasing the resistance of the semiconductor by proton injection.Specifically, protons are injected into only an area in the vicinity ofthe active layer, the area being disposed directly under a ringelectrode. Thereby, a current is concentrated in the active layer thatis disposed directly under the photonic crystal area. Alternatively, aburied hetero-structure formed by crystal regrowth, a current narrowingstructure formed by selective oxidation of an AlAs layer, and the likemay be used as the current narrowing structure.

When a voltage is applied to the electrodes to inject a current into theactive layer, light emitted from the active layer is resonated andamplified in the resonator, resulting in a laser oscillation. The laserbeam is red light with an oscillation wavelength of 670 nm. The currentis concentrated at the central part of the active layer by the currentnarrowing structure formed by a process for increasing the resistance byproton injection, thereby increasing the luminous efficiency.

The mechanism of light reflection at the upper and lower cavity mirrorshas been described. In particular, the lower mirror in which the defectshave been introduced can increase the area of the oscillation spot inthe single mode because of the effect of the defects. In the mirrors,99% or more of the reflectance and the transmittance can betheoretically achieved. However, the mirrors in this embodiment aredesigned so that the periods of holes are shifted by about severalnanometers in order to guide the beam from the direction of the uppercavity mirror. According to this structure, the resonance peak of amirror is slightly shifted, resulting in a decrease in the reflectance.Consequently, the beam is guided in the upward direction.

According to the active layer and the device in this embodiment, a redlaser beam can be obtained using materials composed ofAlGaInP/GalnP/AlGaAs. In addition, III-N semiconductors such asGaN/AlN/InN and mixed crystals thereof; and other Group III-Vsemiconductors such as GaAs/AlAs, InGaAsP/InP, and GaInNAs/AlGaAs andmixed crystals thereof may also be used. Furthermore, Group II-VIsemiconductors such as ZnSe/CdSe/ZnS and mixed crystals thereof may alsobe used. The laser device of this embodiment can provide a single modered laser beam having a large area of 15 μm in diameter. Furthermore,according to the laser device of this embodiment, a reduction in thermalresistance, a reduction in electrical resistance, and a simplificationof production can be achieved as compared with a VCSEL including aresonator with semiconductor DBR mirrors.

Second Embodiment

The structure of a laser device according to a second embodiment willnow be described with reference to FIG. 9. A lower cavity mirror lightconfinement layer 92, a lower cavity mirror layer 93, a lower claddinglayer 94, an active layer 95, and an upper cladding layer 96 aresequentially laminated on a substrate 91. A current narrowing layer 99is provided so as to surround a part of the lower cladding layer 94, theactive layer 95, and a part of the upper cladding layer 96. An uppercavity mirror layer 910 is further laminated on the upper cladding layer96. An n-electrode 911 and a p-electrode 912 are provided on the reverseface of the substrate 91 and on the top face of the upper cavity mirrorlayer 910, respectively. The substrate 91 is an n-type GaAs substratehaving a thickness of 565 μm. The lower cavity mirror layer and thelower cladding layer are composed of n-type Al_(0.4)Ga_(0.6)As and(Al_(0.5)Ga_(0.5))_(0.5)In_(0.5)P, respectively. The upper cavity mirrorand the upper cladding layer are composed of p-type Al_(0.4)Ga_(0.6)Asand (Al_(0.5)Ga_(0.5))_(0.5)In_(0.5)P, respectively.

The distance between the lower and upper cavity mirror layers 93 and 910(i.e., the length of the resonator) is about 1.5 μm (corresponding toabout 7.5 times the wavelength of resonating light). Photonic crystalstructures (holes) 913 and 915 forming mirrors are provided on the lowerand upper cavity mirror layers 93 and 910, respectively. Defects 914 and916 are disposed at the centers of the lower and upper mirrors,respectively. The upper cavity mirror layer 910 is composed of p-typeAl_(0.4)Ga_(0.6)As and has a thickness of 270 nm. The lower cavitymirror layer 93 is composed of n-type Al_(0.4)Ga_(0.6)As and has athickness of 270 nm. The light confinement layer 92 having a lowrefractive index is provided between the lower cavity mirror layer 93and the GaAs substrate 91 having a high refractive index so that lightis effectively confined inside the mirror. The light confinement layer92 is composed of n-type Al_(0.7)Ga_(0.4)As and has a thickness of about1 μm. In this embodiment, the buried hetero-structured current narrowinglayer 99 including an n-type (Al_(0.5)Ga_(0.5))_(0.5)In_(0.5)P sublayer97 and a p-type (Al_(0.5)Ga_(0.5))_(0.5)In_(0.5)P sublayer 98 isprovided. The active layer 95 has a strained quantum well structurecomposed of non-dopedIn_(0.56)Ga_(0.44)P/(Al_(0.5)Ga_(0.5))_(0.5)In_(0.5)P. The number oflayers of the well is three. Each of the In_(0.56)Ga_(0.44)P layer andthe (Al_(0.5)Ga_(0.5))_(0.5)In_(0.5)P layer has a thickness of 6 nm. Then-electrode 911 adjacent to the substrate is composed of Ni/Au/Ge andthe p-electrode 912 adjacent to the mirror is composed of Au—Zn.

A method for producing this structure is the same method as that of thefirst embodiment except that a step of forming the current narrowinglayer 99 of the buried hetero-structure is added.

Specifically, the step is added in the course of the step of forming anAl_(0.9)Ga_(0.4)As lift-off layer and the layers including those fromthe upper cavity mirror layer 910 to the lower cavity mirror layer 93 ona GaAs substrate.

The upper cavity mirror layer 910, the upper cladding layer 96, theactive layer 95, and the lower cladding layer 94 are grown.Subsequently, an area surrounding the light-emitting part of the activelayer 95 is removed by inductively coupled plasma (ICP) dry etchingusing Cl₂ gas. The surrounding area is removed from the lower claddinglayer 94 to the middle of the upper cladding layer 96. The n-type(Al_(0.5)Ga_(0.5))_(0.5)In_(0.5)P sublayer 97 and the p-type(Al_(0.5)Ga_(0.5))_(0.5)In_(0.5)P sublayer 98 are then regrown in thatorder. A planarizing process is then performed, the lower cladding layer94 is continuously grown, and the lower cavity mirror layer 93 is grownon the lower cladding layer 94.

The subsequent steps are the same as those in the first embodiment.

The structures of the cavity mirrors will now be described in detail.

As shown in FIG. 9, the lower and upper cavity mirrors include holes 913and 915 that constitute a basic photonic crystal and defects 914 and 916where holes are not formed, respectively. FIGS. 10A and 10B are planviews of the photonic crystals of the lower and upper mirrors in thisembodiment, respectively.

FIG. 10A shows the lower cavity mirror and FIG. 10B shows the uppercavity mirror.

Features that are common to both upper and lower mirrors will bedescribed. In this embodiment, holes 101 and 103 of a square latticephotonic crystal structure are provided on the entire area of the mirrorlayer surfaces. Defects 102 and 104 that do not include a hole areperiodically positioned at the central circular area with a diameter of15 μm. A defect level is formed within the photonic bandgap only at thisarea. Consequently, light incident on the mirror is reflected by thein-plane guided resonance phenomenon due to the defect level, resultingin an oscillation. It is at the central area of the mirror that thedefects are disposed. In contrast, since such a level is not presentwithin the photonic bandgap at the surrounding area composed of only thebasic photonic crystal, resonance in the direction perpendicular to theplane does not occur, and thus light is not reflected. In addition, thesurrounding photonic crystal structure has a photonic bandgap for lightguided in the in-plane direction and causes reflection. Therefore,leakage of light in the photonic crystal mirror area in the in-planedirection can be prevented.

Different points will be described. In the photonic crystal structure ofthe lower mirror in FIG. 10A, the hole has a round shape, the period is180 nm, the radius of the hole is 75 nm, and the thickness of the layeris 270 nm. The lower mirror layer includes holes 101 and defects 102. Inthe photonic crystal structure of the upper mirror in FIG. 10B, the holehas a rectangular shape, the period is 180 nm, the long side of eachhole is 70 nm, the short side of each hole is 35 nm, and the thicknessof the layer is 270 nm. The upper mirror layer includes holes 103 anddefects 104. When both mirrors disposed on and under the active layerare composed of photonic crystals including minute holes, a claddingmethod can be employed.

In this embodiment, since the holes of the upper mirror have arectangular shape, the symmetry of the photonic crystal structure isdisordered. Consequently, the upper mirror exhibits different reflectioncharacteristics by polarization. Specifically, only polarized lightwhose electric field vector is orientated in the y direction isreflected on the mirror and oscillation occurs, whereas about 100% ofpolarized light whose electric field vector is orientated in the xdirection is transmitted. Thereby, the polarization of laser can becontrolled to achieve an oscillation of single linearly polarized light.Regarding the positional relationship between the upper and lowermirrors, the same relationship as that in the first embodiment issatisfied and the basic conditions for the relationship are the same asthose in the first embodiment.

In response to a current injection from the electrodes, oscillationoccurs in the direction perpendicular to the photonic crystal mirrors asin the first embodiment. The oscillation occurs in the area having adiameter of 15 μm where the photonic crystal mirrors are provided. Alaser beam in the single transverse mode and the single linearpolarization is obtained in this area. The laser beam is red light withan oscillation wavelength of 670 nm. The laser beam is emitted only inthe upward direction by decreasing the reflectance of the upper mirrorto some degree by the same method as that in the first embodiment.

In the laser device according to this embodiment, the spot size and thespot shape in the single mode of the laser beam can be controlled byadjusting the area where the defects of the photonic crystal mirrors aredisposed.

Furthermore, the photonic crystal structure surrounding thedefect-introduced area of the photonic crystal mirror can suppress thelight leakage in the in-plane direction in the mirror, resulting in animprovement in the luminous efficiency of the laser.

In the defect parts of the mirror of this embodiment, holes are notprovided. Alternatively, the defects may be formed by introducing holeseach having a size larger than or smaller than that of the holes of thebasic photonic crystal structure. Alternatively, the defects may beformed by introducing another material having a different refractiveindex into the defect parts.

In addition to AlGaInP/GalnP/AlGaAs, III-N semiconductors such asGaN/AlN/InN and mixed crystals thereof may also be used for thematerials of the device. Furthermore, other Group III-V semiconductorssuch as GaAs/AlAs, InGaAsP/InP, and GaInNAs/AlGaAs; mixed crystalsthereof; Group II-VI semiconductors such as ZnSe/CdSe/ZnS; and mixedcrystals thereof may also be used.

Regarding the arrangement of the mirror with round holes and the mirrorwith rectangular holes, the mirrors may be disposed at positionsopposite to those in this embodiment. Alternatively, both the upper andlower mirrors may be the mirrors with rectangular holes. However, onlywhen both the upper and lower mirrors have rectangular holes, thepositions must be aligned in the rotation direction shown by the γ axisin FIG. 8 showing the positional relationship of the mirrors.Specifically, the rotation axes of both mirrors are adjusted so that thedirections of the vertical axis and the horizontal axis of the rectangleare aligned and the directions of polarization are matched with eachother.

Third Embodiment

A third embodiment will now be described with reference to FIGS. 11A and11B. Since the structure and the materials of the laser device itselfare the same as those in the second embodiment, only the structure ofthe cavity mirrors will be described. The production process is also thesame as that of the second embodiment.

FIGS. 11A and 11B are schematic views of lower and upper photoniccrystal mirrors of the third embodiment, respectively, viewed from adirection perpendicular to a planer surface. As shown in FIG. 11A, inthe lower cavity mirror, holes of a basic photonic crystal structure areprovided in the entire surface, and defects formed by removing the holesare arrayed at the center. Parameters of the basic photonic crystalstructure are the same as those of the lower cavity mirror of the secondembodiment. This embodiment is characterized in the array of thedefects. These defects are arrayed according to a specific regularitybut arrayed aperiodically. Roughly, the defects are concentrated aroundthe central part of the mirror and concentrically arrayed at theperipheral part. Furthermore, as the positions of defects become moredistant from the central part, the interval between the concentriccircles increases. As the positions of defects become more distant fromthe central part, the defect density at the positions is decreased.Accordingly, the defect density is represented by the followingequation:

D=D ₀exp(−r ² /a)  (Equation 1)

wherein D represents the defect density, r represents a distance fromthe center, D₀ represents the defect density at the center of a mirror,and a represents a predetermined constant that determines the magnitudeof a density gradient of the defect from the center. The area of thedefect-introduced area is the same as that in the second embodiment, 15μm in diameter. For the sake of convenience of drawing, the number ofperiods of the concentric defects is very small in FIG. 11A, even thoughdefects are actually arrayed with 10 periods or more. In thistwo-dimensional photonic crystal mirror, the optical density is high atthe central part, which has a high defect density. On the other hand, asthe defect density decreases towards the peripheral part, the opticaldensity also decreases. Consequently, since the defect density in thisembodiment has a profile represented by the Gaussian function asequation 1, the mode profile of the laser beam to be emitted is alsorepresented by the Gaussian function. The upper cavity mirror in FIG.11B is not described because this mirror has the same structure as thatof the lower cavity mirror in the second embodiment.

The surface emitting laser device of this embodiment can provide a laserbeam having a large area of 15 μm in diameter, a single transverse mode,and a single-peaked mode profile.

In the defect parts of the mirror of this embodiment, holes are notprovided. Alternatively, the defects may be formed by introducing holeseach having a diameter larger than or smaller than that of the holes ofthe basic photonic crystal structure. Alternatively, the defects may beformed by introducing another material having a different refractiveindex into the defect parts.

Regarding the array of the defects in the photonic crystal structure, inaddition to the above-described array of the defect density representedby equation 1, for example, as represented by the following equation 2,the defects may be disposed so that the defect density is arranged in aconcentric ellipse pattern.

D=D ₀exp(x ² /a ² +y ² /b ²)  (Equation 2)

wherein a represents the length of the major axis of an ellipse, brepresents the length of the minor axis of the ellipse, and x and yrepresent orthogonal coordinates in a plane.

In addition to AlGaInP/GalnP/AlGaAs, III-N semiconductors such asGaN/AlN/InN and mixed crystals thereof may also be used for thematerials.

Furthermore, other Group III-V semiconductors such as GaAs/AlAs,GaAs/InP, and GaInNAs/AlGaAs; mixed crystals thereof; Group II-VIsemiconductors such as ZnSe/CdSe/ZnS; and mixed crystals thereof mayalso be used.

Furthermore, the upper mirror and the lower mirror of this embodimentmay be replaced with each other. Alternatively, the defect densities ofboth the upper and lower mirrors may have various distributions.

As described above, the defect parts provided in the photonic crystalcan be arrayed on the basis of the above-described mathematicalpatterns.

Fourth Embodiment

The structure of a laser device according to a fourth embodiment willnow be described with reference to FIG. 12.

A lower cavity mirror layer 122, a lower cladding layer 125, an activelayer 126, an upper cladding layer 127, and an upper cavity mirror layer128 are sequentially laminated on a substrate 121. An n-electrode 129and a p-electrode 1213 are provided on the reverse face of the substrate121 and on the top face of the upper cavity mirror layer 128,respectively.

The substrate 121 is an n-type GaAs substrate having a thickness of 300μm. The lower cavity mirror layer 122 has a structure in which firstlayers 123 and second layers 124 are alternately laminated.Specifically, a first n-type Al_(x)Ga_(1-x)As layer (first layer 123)includes a lower sublayer with a thickness of 29 nm wherein x=0.55 andan upper sublayer with a thickness of 20 nm wherein x is varied from0.55 to 0.93. A second Al_(x)Ga_(1-x)As layer (second layer 124)includes a lower sublayer with a thickness of 33.2 nm wherein x=0.93 andan upper sublayer with a thickness of 20 nm wherein x is varied from0.93 to 0.55. Thus, the lower cavity mirror layer 122 is composed of aDBR mirror in which the first layers 123 and the second layers 124 arealternately laminated. Although all the layers are not shown in thefigure, the number of the layers is 70 pairs. As described above, thethickness d of each of the first layers 123 and the second layers 124 isrepresented by Nd=(¼)λ (N: refractive index of substance, λ: wavelengthof resonating light). The upper cavity mirror layer 128 is composed ofp-type Al_(0.4)Ga_(0.6)As. A photonic crystal structure 1211 forming amirror is provided at the center of the upper cavity mirror layer 128and defects 1212 are introduced in the photonic crystal structure 1211.The upper and lower cladding layers 127 and 125 are composed of n-type(Al_(0.5)Ga_(0.5))_(0.5)In_(0.5)P and p-type(Al_(0.5)Ga_(0.5))_(0.5)In_(0.5)P, respectively. The active layer 126has a strained quantum well structure composed of non-dopedGa_(0.56)In_(0.44)P/(Al_(0.5)Ga_(0.5))_(0.5)In_(0.5)P, The number oflayers of the well is three. Each of the Ga_(0.56)In_(0.44)P layer andthe (Al_(0.5)Ga_(0.5))_(0.51)In_(0.49)P layer has a thickness of 6 nm.The distance between the mirrors including the upper and lower claddinglayers 127 and 125 and the active layer 126 (i.e., the length of theresonator) is about 1.5 μm (corresponding to about 7.5 times thewavelength of resonating light). The n-electrode 129 adjacent to thesubstrate is composed of Ni/Au/Ge and the p-electrode 1213 adjacent tothe mirror is composed of Au—Zn.

The above laminated structure is produced as follows. The layers aresequentially formed on a GaAs substrate in the order from the lowercavity DBR mirror to the upper cavity photonic crystal mirror layer byMOCVD. In this embodiment, since the substrate is used without lift-off,the lower cavity mirror is formed first, and other layers are thenlaminated in order. Subsequently, a photonic crystal pattern of theupper cavity mirror layer 128 is formed by EB lithography and RIBE usingCl₂ gas. Finally, the electrodes are formed on the reverse face of theGaAs substrate 121 and on the upper cavity mirror layer 128 by vapordeposition.

In addition to the materials, the structure of this embodiment is alsodifferent from that of the device in the first embodiment in that onlythe upper cavity mirror is changed from the two-dimensional photoniccrystal to the DBR mirror, which is a one-dimensional photonic crystal.Therefore, in this embodiment, in order to achieve a large spot sizewith the single mode, it is necessary that defects are provided in thephotonic crystal structure of the upper mirror. Regarding the structuralparameters of the mirror, the period is 180 nm, the hole diameter is 75nm, and the layer thickness is 250 nm. The emitting spot area has adiameter of 15 μm, which is the same as that in the first embodiment.The defects are formed by removing the holes of the basic photoniccrystal. Alternatively, as described in the first embodiment, holes eachhaving a diameter different from that of the holes of the basic photoniccrystal may be used. Alternatively, the defects may be formed byintroducing another material having a different refractive index intothe defect parts. Regarding the array of the defects, as described inthe first embodiment, the interval between the defects may be larger orsmaller than an interval corresponding to three periods of the photoniccrystal structure. However, when the interval is excessively large,light components localized in the defects cannot be coupled with eachother. Therefore, an upper limit of the interval is present. The porousstructure of the cladding layer or the like may also be provided asdescribed in the first embodiment to the third embodiment. The lowercavity mirror is a known DBR mirror used in a normal VCSEL. Thecharacteristics of the DBR mirror such as the materials of the layers,the thicknesses, and the number of periods may be the same as thosedescribed above.

The relationship between the upper and lower mirrors in this embodimentwill be described. Since the lower cavity mirror does not have apolarization dependence and has a uniform structure in the x, y, and γdirections, precise alignment is not required in the x and y lineardirections and in the γ rotation direction in FIG. 8. Unlike the devicesin the first embodiment to the third embodiment, the necessity of thealignment can be reduced in this embodiment, resulting in an advantagein the production. Regarding the positional relationship in the otherdirections, the same conditions as those described in the otherembodiments are applied to this embodiment.

In this embodiment, a current narrowing structure is formed byincreasing the resistance of the device by proton injection.Specifically, protons are injected into an area disposed directly underthe p-electrode, the area being disposed at the periphery of thephotonic crystal structure. Thereby, a current is concentrated in theactive layer. Alternatively, a buried hetero-structure formed by crystalregrowth, a current narrowing structure formed by selective oxidation ofan AlAs layer in the DBR mirror, and the like may also be used as thecurrent narrowing structure.

When a voltage is applied to the electrodes to inject a current into theactive layer, light emitted from the active layer is resonated andamplified in the resonator, resulting in a laser oscillation. The laserbeam is red light with an oscillation wavelength of 670 nm. Byintroducing defects in the upper cavity mirror, the oscillation spot inthe single mode can be expanded. In this embodiment, the number oflaminations of the upper cavity mirror is adjusted so that thereflectance of the upper cavity mirror is lower than that of the lowercavity mirror.

The known DBR mirror is used as the lower cavity mirror of the surfaceemitting laser device in this embodiment, but the effects such as anincrease in the spot size can be achieved as in the first embodiment.From the viewpoints of the reduction in the thickness, the reduction inthe electrical resistance, and the improvement in the heat dissipationeffect of the device, the laser device in this embodiment is inferior tothat in the first embodiment, but is much superior to the known VCSEL inwhich the DBR mirrors are used as both upper and lower cavity mirrors.

According to this embodiment, by using the known DBR mirror, the devicecan be easily produced at one time by sequentially growing crystals on asubstrate without cladding or the like. Thus, compared with the firstembodiment to the third embodiment, this embodiment is significantlyadvantageous in the production of the device.

Fifth Embodiment

The structure of a laser device according to a fifth embodiment will nowbe described with reference to FIG. 13. A lower cavity mirror layer 132,a lower cladding layer 135, an active layer 136, an upper cladding layer137, and an upper cavity mirror layer 138 are sequentially laminated ona substrate 131. An n-electrode 1311 and a p-electrode 1312 are providedon the reverse face of the substrate 131 and on the top face of theupper cavity mirror layer 138, respectively. The substrate 131 is ann-type GaAs substrate having a thickness of 300 μm. The lower cavitymirror layer 132 is formed by alternately laminating n-typeAl_(0.4)Ga_(0.6)As photonic crystal layers 133 and n-typeAl_(0.4)Ga_(0.6)As spacer layers 134. The upper cavity mirror layer 138is formed by alternately laminating p-type Al_(0.4)Ga_(0.6)As photoniccrystal layers 139 and p-type Al_(0.4)Ga_(0.6)As spacer layers 1310.Each of the upper and lower mirrors is composed of four layers includingtwo pairs. Holes 1313 and 1314 are periodically provided for every otherlayer to form photonic crystal mirrors. The spacer layers are providedin order to adjust the phases between the photonic crystal mirrors. Theupper and the lower cladding layers are composed of n-type(Al_(0.5)Ga_(0.5))_(0.5)In_(0.5)P and p-type(Al_(0.5)Ga_(0.5))_(0.5)In_(0.5)P, respectively. The active layer 136has a strained quantum well structure composed of non-dopedGa_(0.56)In_(0.44)P/(Al_(0.5)Ga_(0.5))_(0.5)In_(0.5)P. The number oflayers of the well is three. Each of the Ga_(0.56)In_(0.44)P layer andthe (Al_(0.5)Ga_(0.5))_(0.5)In_(0.5)P layer has a thickness of 6 nm. Thedistance between the mirrors including the active layer 136 (i.e., thelength of the resonator) is about 1.5 μm (corresponding to about 7.5times the wavelength of resonating light). The n-electrode 1311 adjacentto the substrate is composed of Ni/Au/Ge and the p-electrode 1312adjacent to the mirror is composed of Au.

The above laminated structure is produced as follows. An AlAs lift-offlayer is formed on a GaAs substrate and a layer adjacent to theresonator of the upper cavity mirror layer 138 is formed on the lift-offlayer by MOCVD. The upper cladding layer 137, the active layer 136, thelower cladding layer 135, and a layer adjacent to the resonator of thelower cavity mirror layer 132 are sequentially formed thereon. Theresulting wafer is referred to as wafer A. Since the GaAs substrate islifted off from wafer A in a later process, the layers are formed in theorder opposite to that in the actual device. In this step, among thecavity mirror layers, only the single layer that is in contact with eachcladding layer is formed.

Subsequently, the lower cavity mirror layer 132 is prepared. A photoniccrystal pattern is formed on the lower cavity mirror layer of wafer A bythe same method as that in the fourth embodiment. An AlAs lift-off layeris formed on another GaAs substrate and an Al_(0.4)Ga_(0.6)As spacerlayer 134 is formed on the lift-off layer. The resulting substrate isjoined on the lower cavity mirror layer of wafer A by thermal fusionbonding. The GaAs substrate is then lifted off by selectively etchingthe AlAs lift-off layer with hydrofluoric acid, thereby forming thespacer layer 134 of the lower cavity mirror layer. Subsequently, anAl_(0.4)Ga_(0.6)As layer is formed on wafer A again, and a photoniccrystal is patterned thereon. Furthermore, another spacer layer 134 isjoined on the photonic crystal layer again. A GaAs substrate having onlyan Al_(0.4)Ga_(0.6)As layer is used in this step. In bonding of thisspacer layer, since the GaAs substrate need not be lifted off, an AlAslift-off layer need not be provided on the wafer to be bonded. Thus, theformation of the lower cavity mirror is completed.

A method for preparing the upper cavity mirror layer 138 will bedescribed. The GaAs substrate that is used from the start in thepreparation of wafer A (which is not the substrate bonded in thesubsequent step) is lifted off by selectively etching the AlAs lift-offlayer. A photonic crystal is then patterned on the surface layeradjacent to the resonator of the upper cavity mirror by the same methodas that described above to form a photonic crystal layer adjacent to theresonator of the upper cavity mirror. Subsequently, two pairs of layersconstituting the upper cavity mirror are formed by the same method asthat of the lower cavity mirror. However, unlike the lower cavitymirror, the GaAs substrate remaining until the last step is also liftedoff in this upper cavity mirror. Thus, the formation of the upper cavitymirror is completed.

A laser cavity is prepared by the above process. Finally, electrodes areformed on the reverse face of the GaAs substrate and on the upper cavitymirror by vapor deposition.

The cavity mirrors of this embodiment will now be described in detail.

The lower and upper cavity mirrors include Al_(0.4)Ga_(0.6)As photoniccrystal layers and Al_(0.4)Ga_(0.6)As spacer layers. Regarding thestructural parameters of the photonic crystal mirrors, the period is 180nm, the hole diameter is 75 nm, and the layer thickness is 250 nm.Defects 1315 are introduced in one of the photonic crystal mirrorsconstituting the upper cavity mirror layer 138 by periodically removingthe holes. The emitting spot area including the photonic crystalstructure has a diameter of 15 μm. Each pair composed of the photoniccrystal layer and the spacer layer is designed so that the phase of thereflected light proceeds by (n/2) wavelengths per pair. The pair isdesigned so that the phase of light reflected on the photonic crystallayer 139 and the phase of light reflected on the photonic crystalprovided on the photonic crystal layer 139 are matched in the interfacebetween the photonic crystal layer 139 and the upper cladding layer 137.Specifically, the phase of light reflected by the in-plane guidedresonance is constant when the light is emitted from the photoniccrystal. Therefore, the thickness of the spacer layer is adjusted suchthat the phase matching condition is satisfied by two pairs. The spacerlayer in this embodiment has a thickness of 48 nm.

The positional relationship between the photonic crystal mirrors in FIG.8 will be described. The relationship between the upper cavity mirrorlayer 138 and the lower cavity mirror layer 132 is the same as that inthe first embodiment, the third embodiment, and the fourth embodiment.On the other hand, in each cavity mirror layer, the distance between thephotonic crystal mirrors in this embodiment is short, i.e., ahalf-wavelength of the wavelength of the emitted laser light. Therefore,light components guided in adjacent photonic crystal mirrors in thecavity mirror layer in the in-plane direction are coupled with eachother. Accordingly, the positional relationship between the mirrors mustbe adjusted so as to be the same in the x, y, and γ directions in FIG.8.

In addition to the defects described in this embodiment, holes eachhaving a diameter different from that of the basic photonic crystal mayalso be used as the defects. Alternatively, the defects may be formed byintroducing another material having a different refractive index intothe defect parts. Regarding the array of the defects, the intervalbetween the defects may be larger or smaller than an intervalcorresponding to three periods of the photonic crystal structure.

In this embodiment, the defects are introduced in only one of thephotonic crystal mirrors constituting either the upper cavity mirrorlayer or the lower cavity mirror layer. Alternatively, the defects maybe introduced in both the upper cavity mirror layer and the lower cavitymirror layer. In addition, the defects may be introduced in two photoniccrystal mirrors constituting each of the upper cavity mirror layer andthe lower cavity mirror layer.

A current narrowing structure in this embodiment is also formed byincreasing the resistance of the device by proton injection.Specifically, protons are injected into an area disposed directly underthe p-electrode, the area being disposed at the periphery of thephotonic crystal structure. Thereby, a current is concentrated in theactive layer. Alternatively, a buried hetero-structure formed by crystalregrowth, a current narrowing structure formed by selective oxidation ofan AlAs layer in the DBR mirror, and the like may also be used as thecurrent narrowing structure.

The behavior in the response of a current injection is the same as thatin the fourth embodiment.

Use of the surface emitting laser device in this embodiment can increasethe reflectance of the cavity mirrors, compared with a device includinga single photonic crystal mirror. Consequently, the threshold currentcan be decreased. Furthermore, even when the reflectance of each mirrordoes not satisfy the desired value because of errors in the productionor the like, higher reflectance can be achieved by laminating aplurality of the mirrors.

Sixth Embodiment

The structure of a laser device according to a sixth embodiment will nowbe described with reference to FIG. 15. FIG. 15 shows an upper mirror inthe laser device according to this embodiment. A photonic crystalstructure 15141 composed of a square lattice is provided in a circulararea having a diameter of 15 μm at the center of a mirror layer. Theperiphery of the photonic crystal structure 15141 is surrounded by aphotonic crystal structure 15142 composed of a triangular lattice.Defects are periodically introduced in the photonic crystal structure15141. The structure of the laser device is the same as that in thesecond embodiment except for this upper mirror. In this embodiment, thestructure is prepared such that the defect level of the photonic crystalstructure 15141 corresponds within the photonic bandgap of the photoniccrystal structure 15142. As a result, the leakage of light in the mirrorarea in the in-plane direction can be suppressed by the same principleas that described in the second embodiment. This embodiment is differentfrom the second embodiment in that the basic photonic crystal structuresare different between the central area functioning as a mirror and theperipheral area suppressing the light leakage. In this case, a featureof the square lattice that the design is relatively simple and a featureof the triangular lattice that the photonic bandgap is generally largerthan that of the square lattice (i.e., the light leakage is suppressedmore effectively) can be combined. FIGS. 16A and 16B show examples of aphotonic band structure of a two-dimensional photonic crystal. Thecalculation was performed on the basis of a structure in which holes(refractive index: 1.0) each having a radius of 0.3a are periodicallyarrayed in a solid medium (refractive index: 3.46). The abscissaindicates a wave number vector and the ordinate indicates a normalizedfrequency of light. FIG. 16A shows a photonic band structure of a squarelattice and FIG. 16B shows a photonic band structure of a triangularlattice. The comparison between FIG. 16A and FIG. 16B shows that aphotonic bandgap 166 is present in the triangular lattice, whereas suchphotonic bandgap is not present in the square lattice. In other words,in order to suppress the light leakage in the in-plane direction moreeffectively, the triangular lattice can be generally used rather thanthe square lattice. In this embodiment, the structure combining thetriangular lattice and the square lattice is used only in the uppermirror. Alternatively, this structure may be used only in the lowermirror or both upper and lower mirrors.

Referring to FIG. 14A, in a two-dimensional photonic crystal slab 1401,a square lattice photonic crystal composed of rectangular square holes1403 is provided at the central part and a photonic crystal composed ofcylindrical holes 1402, which block light by the photonic bandgapeffect, is provided around the square lattice photonic crystal. FIG. 14Bis a cross-sectional view taken along line XIV B-XIV B in FIG. 14A.According to this structure, light that can be present at the centralpart is blocked by the surrounding photonic crystal, thereby decreasingan optical loss in the two-dimensional direction. The cylindrical holes1402 are arrayed in a triangular lattice form and the square holes 1403are arrayed in a square lattice form.

Seventh Embodiment

A periodic-refractive-index structure 7106 including two layersaccording to the present invention will now be described with referenceto FIG. 17. The feature of this embodiment is that a part that disordersthe periodicity of the periodic-refractive-index structure is formed bya second layer 7110 adjacent to a first layer 7109 having a periodicstructure. FIG. 17 shows the structure of a two-dimensional photoniccrystal surface emitting laser of this embodiment. In FIG. 17, thesurface emitting laser includes a substrate 7100, a first mirror 7102, aquantum well active layer 7104, and a second mirror (two-dimensionalphotonic crystal) 7106.

The surface emitting laser of this embodiment is formed so that theantinode of standing waves formed in the resonator is disposed atboundaries between the active layer and the upper mirror (second mirror)and between the active layer and the lower mirror (first mirror), and atthe center of the resonator. The quantum well active layer 7104 isprovided at the center of the resonator and is formed so as to performgain matching. In this embodiment, the first mirror 7102 is a multilayerfilm reflective mirror produced by alternately laminating ahigh-refractive-index medium having a thickness of ¼ wavelength and alow-refractive-index medium having a thickness of ¼ wavelength. Theabove-described two-dimensional photonic crystal mirror to which thepresent invention is applied is used as the second mirror. In thetwo-dimensional photonic crystal mirror of this embodiment, the firstlayer 7109 composed of a first two-dimensional periodic structure andthe second layer 7110 composed of a second two-dimensional periodicstructure are disposed so as to be in contact with each other.

In the first layer 7109 composed of the first two-dimensional periodicstructure, columnar structures 7509 composed of a second medium having asecond refractive index are periodically provided at a certain intervalin a first medium having a first refractive index. In the second layer7110 composed of the second two-dimensional periodic structure, columnarstructures 7510 composed of a fourth medium having a fourth refractiveindex are provided in a third medium having a third refractive index atan interval different from the periodicity of the columnar structures7509 composed of the second medium. As a result, the use of such firstand second layers can disorder the periodicity of the first layer. Fromthe standpoint of disordering the periodicity, the pore sizes of thecolumnar structures (composed of, for example, holes) provided in thefirst layer and the second layer are preferably determined so as to bedifferent from each other. The second layer 7110 does not necessarilyrequire a periodicity as long as the second layer 7110 has a function ofdisordering the periodicity of the first layer 7109.

A method of producing the two-dimensional photonic crystal mirror inthis embodiment will be described. FIGS. 18A to 18H include schematicviews showing steps of producing the two-dimensional photonic crystalmirror of this embodiment. In FIGS. 18A to 18H, reference numeral 8200indicates a sapphire substrate and reference numeral 8202 indicates afirst nitride semiconductor layer. In the figures, reference numeral8204 indicates a first resist pattern, reference numeral 8510 indicatesfirst columnar holes, reference numeral 8208 indicates a secondsemiconductor layer, reference numeral 8210 indicates a third nitridesemiconductor layer (p-GaN layer), reference numeral 8212 indicates asecond resist pattern, and reference numeral 8509 indicates secondcolumnar holes.

The two-dimensional photonic crystal mirror is produced as follows.First, on the sapphire substrate 8200, a GaN/AlGaN-DBR mirror layer, ann-AlGaN cladding layer, a InGaN/AlGaN-MQW active layer, a p-AlGaNcladding layer, and a p-GaN layer are grown in that order using ametalorganic chemical vapor deposition (MOCVD) system, with a bufferlayer provided between the sapphire substrate 8200 and the GaN/AlGaN-DBRmirror layer. Thus, the first nitride semiconductor layer 8202 is formed(FIG. 18A).

Subsequently, the first resist pattern 8204 is formed on the p-GaN layerby photolithography or electron beam lithography (FIG. 18B).

Subsequently, the p-GaN layer of the first nitride semiconductor layer8202 is dry-etched with a reactive ion beam etching system to form thefirst columnar holes 8510 (FIG. 18C). The first columnar holes 8510 areformed so as to have a periodicity different from that of the secondcolumnar holes 8509 in the third nitride semiconductor layer 8210 formedin the subsequent step.

Next, silicon nitride or silicon oxide is embedded in the first columnarholes 8510 formed in FIG. 18C to form the second semiconductor layer8208 (FIG. 18D). In this step, silicon nitride or silicon oxide isdeposited with a sputtering system or a chemical vapor deposition (CVD)system. The second semiconductor layer 8208 composed of silicon nitrideor silicon oxide is then formed only in the first columnar holes 8510.Specifically, silicon nitride is deposited on the entire surfaces of thefirst columnar holes 8510 and the first resist pattern 8204, and theresist is removed to lift off the silicon nitride disposed on theresist. Alternatively, a mask may be separately prepared, and siliconnitride may be deposited only in the first columnar holes 8510.

Next, the p-GaN layer, which is the third nitride semiconductor layer8210, is grown with an MOCVD system or an molecular beam epitaxy (MBE)system on the p-GaN layer, which is the first nitride semiconductorlayer 8202 in which silicon nitride or silicon oxide is embedded in thefirst columnar holes 8510 (FIG. 18E).

Subsequently, a resist pattern is formed on the p-GaN layer by electronbeam lithography (FIG. 18F). As shown in FIG. 18F, the second resistpattern 8212 formed in this step is not disposed on the silicon nitrideor silicon oxide parts formed in the step shown in FIG. 18D.

Subsequently, the p-GaN layer is dry-etched with a reactive ion beametching system to form the second columnar holes 8509 (FIG. 18G). Unlikethe above-described first columnar holes 8510, the second columnar holes8509 are periodically formed at a certain interval. Regarding theetching depth in this step, the etching is performed until the siliconnitride or silicon oxide parts formed in the step shown in FIG. 18D areexposed.

The exposed silicon nitride or silicon oxide parts are selectivelyremoved by etching (FIG. 18H).

Thus, a photonic crystal structure including a second layer 8110 havingthe first columnar holes 8510 and a first layer 8109 having the secondcolumnar holes 8509 is produced. The second layer 8110 has a structurethat disorders the periodicity of the first layer 8109.

In this embodiment, silicon nitride is deposited in the hole parts, butthe present invention is not limited thereto. Alternatively, siliconoxide, magnesium oxide, aluminum oxide, or the like may also be used. Inthis embodiment, silicon nitride formed in the hole parts is removed,however, silicon nitride does not necessarily have to be removed. Thatis, the columnar holes in FIG. 18D may be filled with a certain medium.This embodiment describes a two-dimensional photonic crystal surfaceemitting laser including a nitride semiconductor, but the presentinvention is not limited to such a nitride semiconductor. The presentinvention can also be applied to, for example, a gallium-arsenic orindium-phosphorus semiconductor. The present invention can be applied toa surface emitting laser with a wavelength ranging from the ultravioletto infrared region.

FIG. 19 is a conceptual cross-sectional view of the two-dimensionalphotonic crystal surface emitting laser produced in this embodiment. Inthis structure, etching for forming posts is performed with a reactiveion beam etching system, and cathodes 9700 and anodes 9702 are thenformed. In this embodiment, the resonator includes a DBR mirror layer9500 composed of a laminate of GaN/AlGaN and a two-dimensional photoniccrystal mirror 9600 having a periodic defect, but the present inventionis not limited to this structure.

The surface emitting laser according to the present invention can beused as a light source in the industrial fields such as an opticalcommunication technology, an electrophotographic technology, a displaydevice technology, and a mass storage medium.

Although exemplary embodiments of this invention have been described indetail above, those skilled in the art will be readily appreciated thatmany modifications are possible in the exemplary embodiments withoutmaterially departing from the novel teachings and advantages of thisinvention. Accordingly, all such modifications are intended to beincluded within the scope of this invention. The scope of the followingclaims is to be accorded the broadest interpretation so as to encompassall modifications, equivalent structures and functions.

This application claims the benefit of Japanese Application No.2005-131643 filed Apr. 28, 2005, No. 2005-130718 filed Apr. 28, 2005,No. 2006-052935 filed Feb. 28, 2006 and No. 2005-233776 filed Aug. 11,2005, which are hereby incorporated by reference herein in theirentirety.

1. A vertical cavity surface emitting laser device comprising: a firstreflective mirror; a second reflective mirror having aperiodic-refractive-index structure in which the refractive indexperiodically changes in the in-plane direction of a plane opposing thefirst reflective mirror; and an active layer disposed between the firstreflective mirror and the second reflective mirror, wherein theperiodic-refractive-index structure includes a plurality of parts thatdisorder the periodicity of the periodic-refractive-index structure ofthe second reflective mirror and wherein the periodic-refractive-indexstructure is structured such that light incident on theperiodic-refractive-index structure in the perpendicular direction tothe in-plan direction of the periodic-refractive-index structure causesresonance in the in-plane direction and the light is emitted in thedirection perpendicular to the in-plane direction.
 2. The verticalcavity surface emitting laser device according to claim 1, wherein theperiodic-refractive-index structure is a two-dimensional photoniccrystal structure.
 3. The vertical cavity surface emitting laser deviceaccording to claim 2, wherein a defect level is present within aphotonic bandgap of the two-dimensional photonic crystal structurecorresponding to the parts that disorder the periodicity of theperiodic-refractive-index structure.
 4. The vertical cavity surfaceemitting laser device according to claim 1, wherein the parts thatdisorder the periodicity of the periodic-refractive-index structure arepositioned periodically or aperiodically in the in-plane direction ofthe second reflective mirror.
 5. The vertical cavity surface emittinglaser device according to claim 1, wherein the parts that disorder theperiodicity of the periodic-refractive-index structure includelight-emitting parts that are optically coupled with each other, whereinthe vertical cavity surface emitting laser device emits light in thesingle transverse mode.
 6. The vertical cavity surface emitting laserdevice according to claim 1, wherein the first reflective mirror, theactive layer, and the second reflective mirror having theperiodic-refractive-index structure are disposed on a substrate in thatorder and the first reflective mirror comprises a multilayer film. 7.The vertical cavity surface emitting laser device according to claim 1,wherein the second reflective mirror, the active layer, and the firstreflective mirror are disposed on a substrate in that order and thefirst reflective mirror comprises a multilayer film.
 8. The verticalcavity surface emitting laser device according to claim 1, wherein thefirst reflective mirror, the active layer, and the second reflectivemirror having the periodic-refractive-index structure are disposed on asubstrate in that order and both the first reflective mirror and thesecond reflective mirror comprise a two-dimensional photonic crystal. 9.The vertical cavity surface emitting laser device according to claim 1,wherein the first reflective mirror, the active layer, the secondreflective mirror having the periodic-refractive-index structure, and anelectrode are disposed on a substrate in that order and theperiodic-refractive-index structure is not provided in a part of thesecond reflective mirror disposed directly under the electrode.
 10. Thevertical cavity surface emitting laser device according to claim 1,wherein the second reflective mirror comprises a plurality of layerseach having a periodic-refractive-index structure.
 11. The verticalcavity surface emitting laser device according to claim 1, wherein theperiodic-refractive-index structure comprises a first medium and asecond medium, the second medium having a refractive index higher thanthat of the first medium, and wherein the device further comprises alayer comprising a medium having a refractive index lower than that ofthe second medium disposed between the second reflective mirror havingthe periodic-refractive-index structure and the active layer.
 12. Thevertical cavity surface emitting laser device according to claim 1,wherein the first reflective mirror is a distributed Bragg reflectormirror comprising a multilayer film.
 13. The vertical cavity surfaceemitting laser device according to claim 1, wherein the interval betweenthe parts that disorder the periodicity of the periodic-refractive-indexstructure is set so that the parts that disorder the periodicity serveas light-emitting parts and light components in each of the parts thatdisorder the periodicity are coupled with each other.
 14. The verticalcavity surface emitting laser device according to claim 1, wherein theperiodic-refractive-index structure comprises a first area in which theparts that disorder the periodicity are disposed and a second area inwhich the parts that disorder the periodicity are not disposed, and thesecond area is positioned so as to surround the first area.
 15. Thevertical cavity surface emitting laser device according to claim 14,wherein the first area comprises a square lattice and the second areacomprises a triangular lattice.
 16. The vertical cavity surface emittinglaser device according to claim 1, wherein the periodic-refractive-indexstructure comprises a two-dimensional photonic crystal and the partsthat disorder the periodicity are defects. 17-21. (canceled)
 22. Avertical cavity surface emitting laser device according to claim 1,wherein an energy level of a plurality of parts that disorder the periodis positioned within 50% from the center of a photonic bandgap of theperiodic-refractive-index structure in a range between the center andthe band edge of the photonic bandgap.